Palgrave Handbook of Econometrics: Applied Econometrics

William Greene 535

comparing the different negative binomial models, note that NB2 is the worst
of the three by the likelihood function, though NB1 and NB2 are not directly
comparable. On the other hand, in the NBP model, the estimate ofPis more
than 10 standard errors from 1 or 2, so both NB1 and NB2 would be rejected in
favor of the unrestricted NBP form of the model. The NBP and the heterogeneous
NB2 model are not nested either, but on comparing the log-likelihoods, it does
appear that the heterogeneous model is substantially superior. We computed the
Vuong statistic based on the individual contributions to the log-likelihoods, with
vi=lnLi(NBP) – lnLi(NB2 – H). The value of the statistic is−3.27. On this basis, we
would reject NBP in favor of NB2–H. Finally, with regard to the original question,
the coefficient on PUBLIC is larger than 10 times its estimated standard error in
every specification. We would conclude that the results are consistent with the
proposition that there is evidence of moral hazard.
Estimates of the two two-part models, zero inflated and hurdle, are presented in
Table 11.8. The regime equation for both is assumed to be a logit binary choice
model with:

zit=(1,Age, Female, Married, Kids, Income, Self-employed).

There is little theoretical basis for choosing between the two models. The inter-
pretation of the data-generating process is quite similar in both cases. Each posits
a regime in which the individual chooses whether or not to “participate” in the

Table 11.8 Two-part models for DocVis

Poisson Poisson/logit zero inflation Poisson/logit hurdle

Variable Count Count Regime Count Regime

Constant 0.7162

(0.03287)

1.3689

(0.01338)

0.4789

(0.0651)

1.4187

(0.0128)

–0.5105

(0.0637)

Age 0.01844

(0.000332)

0.01067

(0.00013)

–0.01984

(0.00133)

0.01059

(0.00012)

0.02068

(0.00131)

Education –0.03429

(0.00180)

–0.02038

(0.00075)

0.0000

(0.0000)

–0.02215

(0.00072)

0.0000

(0.0000)

Income –0.4751

(0.02198)

–0.4131

(0.00869)

0.1663

(0.0758)

–0.4560

(0.00831)

–0.2499

(0.0724)

Kids –0.1582

(0.00796)

–0.08639

(0.00316)

0.2306

(0.0303)

–0.08862

(0.00297)

–0.2378

(0.0297)

Public 0.2364

(0.0133)

0.1573

(0.00604)

0.0000

(0.0000)

0.1547

(0.006037)

0.0000

(0.0000)

Female 0.0000

(0.0000)

0.0000

(0.0000)

–0.58789

(0.0265)

0.0000

(0.0000)

0.5812

(0.0260)

Married 0.0000

(0.0000)

0.0000

(0.0000)

–0.1257

(0.0342)

0.0000

(0.0000)

0.1271

(0.0336)

Self-employed 0.0000

(0.0000)

0.0000

(0.0000)

0.4172

(0.0521)

0.0000

(0.0000)

–0.4137

(0.0513)

log-likelihood –104440.3 –83648.75 –83988.80